Classical fairness metrics such as Statistical Parity [1]}, Equality of Opportunity [2]}, and Predictive Parity [3]} work well when exhaustive ground truth is readily available.
For non-exhaustive ground truth, these metrics would need to presume that the absence of a label implies the data point is negative for that label, which can be problematic.
For example, an image of a car without a butterfly label would imply the absence of a butterfly without actually having this ground truth.
This could encode biases that ground-truth-dependent fairness metrics would by definition be unable to detect (in this case, that butterflies never appear in images with cars).
Thus, as ML models and datasets grow in size and label sparsity becomes more common, alternative ways to measure biases complementing ground-truth-dependent approaches must be used.
One approach uses correlation metrics as a proxy for bias in these settings [4]}.
These metrics measure the co-occurrence of two features or predictions in a single data point (akin to the bag-of-words model in NLP [5]}).
Using such metrics, one can calculate fairness scores for individual labels in large label spaces by comparing a label's co-occurrence rate between labels and sensitive attributes (e.g. compare the co-occurrence of basketball with gender directions).
Such metrics can be used to measure bias in both datasets and model predictions.
In the model context, one may wish to measure whether a classifier assigns a label at a high level relative to chance expectation for a direction of a sensitive attribute.
For datasets, we are interested in measuring the correlation between labels assigned to a data point and sensitive attribute directions, whereas label assignment can be through human annotators or other algorithmic approaches.
Correlation calculation can be done between different data labels or predictions of a multi-label classification model (e.g. scientist and earring).
Another option to calculate this correlation is between a data label or model prediction and another known attribute recoverable from metadata, such as geo-tags, time of capture, or even predictions from another neural network.
